The meeting came two weeks after a Hizbullah rocket cache in a home in the village of Khirbat a-Silm accidentally exploded.
Graziano said the focus of UNIFIL's activity was on preventing violations of Security Council Resolution 1701.
"UNIFIL acts in a transparent way and keeps UN Headquarters and the parties fully and factually informed on all the developments on the ground and any violations of Resolution 1701," he said.
According to Lebanese media reports, Amal Movement MP Ali Bazzi and Hizbullah MP Hassan Fadlallah were present at the meeting with the UNIFIL commander. According to UNIFIL, Graziano said he was committed to working with the Lebanese to maintain calm in the region.
"We must remember two fundamental facts that have been established over all these years of UNIFIL's presence in south Lebanon: One, that we are here for the people of south Lebanon. Two, that the UN Security Council has given us a mandate that we must implement on the ground," Graziano said.
Israeli defense officials said that Graziano, an Italian general, was scheduled to complete his term as commander of UNIFIL by the end of the year and was hoping to secure a top post in the United Nations. To do this, the officials said, Graziano was hoping to keep a lid on the tense situation in Lebanon at least until the end of his term.
"UNIFIL should focus on cracking down on Hizbullah instead of meeting with representatives of the terrorist organization," an Israeli defense official said, noting that Israel was working to "sharpen" UNIFIL's mandate to allow the force to sweep villages without coordinating with the Lebanese beforehand.
Meanwhile, amid reports of growing tension along the northern border and predictions by Hizbullah chief Sheikh Hassan Nasrallah that Israel would attack Lebanon, IDF Chief of General Staff Lt.-Gen. Gabi Ashkenazi said there were no "winds of war" blowing along the northern border.
"We are closely following what is happening along the northern border," Ashkenazi said during a tour of the Tel Hashomer IDF Induction Center. "In general, there is quiet there, and I am not aware of any winds of war in the region.
"The explosion in southern Lebanon proves our claims that Hizbullah is bolstering its offensive capabilities in southern Lebanon villages," he continued. "We view this [event] gravely, [considering that this area] is under the watch of UNIFIL and the Lebanese government."
A senior IDF officer said that the source of the tension was a decision by Hizbullah to overtly deploy some of its fighters along the border with Israel near the Shaba Farms earlier this week. Israel responded accordingly and also beefed up its military presence in the area.
According to Lebanese media reports, the IDF moved four Merkava tanks into the area and flew a number of aircraft overhead throughout the day.
Nevertheless, the assessment in the IDF is that Hizbullah is not interested in a new conflict with Israel, but is still doing its utmost to launch an attack against a Jewish or Israeli site abroad to avenge the 2008 assassination of Hizbullah military chief Imad Mughniyeh.
"Hizbullah wants to strike at us, but is concerned what our response will be if a synagogue or an embassy is attacked somewhere overseas," a defense official said. "It is concerned that such an attack would lead to an all-out war, which is something it will want to avoid."
Thus, if such an attack is perpetrated - Hizbullah has reportedly tried to attack the embassy in Azerbaijan - the assessment is that the group will not take direct responsibility, but will instead use a proxy. At the same time, Hizbullah will also likely denounce the attack.